Problem: Simplify; express your answer in exponential form. Assume $y\neq 0, z\neq 0$. $\dfrac{{(y^{-2})^{-2}}}{{(y^{4}z^{-1})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{-2}}$ to the exponent ${-2}$ . Now ${-2 \times -2 = 4}$ , so ${(y^{-2})^{-2} = y^{4}}$ In the denominator, we can use the distributive property of exponents. ${(y^{4}z^{-1})^{2} = (y^{4})^{2}(z^{-1})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{-2})^{-2}}}{{(y^{4}z^{-1})^{2}}} = \dfrac{{y^{4}}}{{y^{8}z^{-2}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{4}}}{{y^{8}z^{-2}}} = \dfrac{{y^{4}}}{{y^{8}}} \cdot \dfrac{{1}}{{z^{-2}}} = y^{{4} - {8}} \cdot z^{- {(-2)}} = y^{-4}z^{2}$.